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Article overview
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Relative Volume Rigidity in Alexandrov Geometry | Nan Li
; Xiaochun Rong
; | Date: |
23 Jun 2011 | Abstract: | Given a compact Alexadrov $n$-space $Z$ with curvature curv $ge kappa$, and
let $f: Z o X$ be a distance non-increasing onto map to another Alexandrov
$n$-space with curv $ge kappa$. The {it relative volume rigidity conjecture}
says that if $X$ achieves the relative maximal volume i.e.
$ ext{vol}(Z)= ext{vol}(X)$, then $X$ is isometric to $Z/sim$, where $z,
z’inpartial Z$ and $zsim z’$ if only if $f(z)=f(z’)$. We will partially
verify this conjecture, and give a classification for compact Alexandrov
$n$-spaces with relatively maximal volume. We will also give an elementary
proof for a pointed version of Bishop-Gromov relative volume comparison with
rigidity in Alexandrov geometry. | Source: | arXiv, 1106.4611 | Services: | Forum | Review | PDF | Favorites |
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